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Application of wavelets in few-body problems.
Hewawasam, Kuravi (2012)

Application of wavelets in few-body problems.


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Thesis or Dissertation

This study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem.

University of Minnesota M.S. thesis. August 2012. Major: Physics. Advisor: John R Hiller. 1 computer file (PDF); viii, 82 pages, appendices A-B.

Suggested Citation
Hewawasam, Kuravi. (2012). Application of wavelets in few-body problems.. Retrieved from the University of Minnesota Digital Conservancy,

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